7. (10 points) Use Columns C and D for this question. (Column C and D are in bol

Question

7. (10 points) Use Columns C and D for this question. (Column C and D are in bold)

You are measuring car speeds using two different radar guns C and D. You want to know whether there is any difference in the speed depending on which radar gun is used. Column C gives the speed using radar gun C. Column D gives the speed for the SAME car using radar gun D. Now there are two ways to do the problem. We could test if µ(C) is equal to µ(D). Or since there is data for the same car using different radar guns, we could test whether µ(C-D) = 0.

The easier way to do this problem is to test whether µ(C-D) = 0, or µ(C-D) 0.

a. Make a new series of data samples by letting E = C – D. List your new series of 7 numbers.

b. What is the null hypothesis H0 ?

c. What is the alternative hypothesis Ha ?

d. What type of tail test are we going to use? (left tail, right tail, two tail)

e. What is the mean xbar of this new sample?

f. What is the standard deviation of the sample s?

g. What is the size of the sample n?

h. How many degrees of freedom does this data set have?

i. What is the t-statistic for this sample?

j. Use the t-distribution calculator to compute a p-value. Show a screen shot of your answer.

k. Based on this value of p and using a 90% confidence level, is there a systematic difference in the car speeds as measured by the two radar guns? Should we accept or reject the null hypothesis?

-1 45 47 2000 15 2 50 51 2002 20 -3 61 62 2004 22 1 75 74 2006 26 -1 25 27 2008 33 0 37 40 2010 34 -4 55 54 2012 37 5 2014 45 -2 2016 47 1 -3 2 -1 2 -4 3 0 1 -2 2

Explanation / Answer

sOLUTIONa:

sOLUTIONb:

nULL HYPOTHESIS:

Ho: µ(C-D) = 0

SolutionC:

Alternative Hypothesis

H1: µ(C-D) 0.

sOLUTIOND:

Its a two tail test since its is non directional

SolutionE:

mean of new sample

xbar(E)=sum/total=-7/7

mean =-1

Solutionf:

Std deviation=1.527

Solutiong:

size of sample=n=7

Solutionh:

Degrees of freedom=n-1=7-1=6

C D E=C-D 45 47 -2 50 51 -1 61 62 -1 75 74 1 25 27 -2 37 40 -3 55 54 1

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